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Hodge cohomology of some foliated boundary and foliated cusp metrics
Author(s) -
GellRedman Jesse,
Rochon Frédéric
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300076
Subject(s) - mathematics , fibration , fibered knot , pure mathematics , cusp (singularity) , boundary (topology) , cohomology , foliation (geology) , space (punctuation) , metric (unit) , mathematical analysis , geometry , homotopy , linguistics , philosophy , geochemistry , metamorphic rock , geology , operations management , economics
For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of L 2 harmonic forms of fixed degree with the images of maps between intersection cohomology groups of an associated stratified space obtained by collapsing the fibres of the fibration at infinity onto its base. In the present paper, we obtain a generalization of this result to situations where, rather than a fibration at infinity, there is a Riemannian foliation with compact leaves admitting a resolution by a fibration. If the associated stratified space (obtained now by collapsing the leaves of the foliation) is a Witt space and if the metric considered is a foliated cusp metric, then no such resolution is required.